Computer controlled rolling mill

ABSTRACT

A computer controlled rolling mill is described wherein the force (or power) model in the computer is stored as dual curves, i.e., (a) shaping curves wherein the ratio of the force required for actual rolling conditions relative to the force required for a chosen draft is plotted against elongation, and (b) magnitude curves wherein the force required for the chosen draft is plotted against inverse output thickness from the mill with each point of the magnitude curves having an associated stored temperature value. The arithmetic produce of the force ratio required for a desired elongation and the force magnitude for a desired output thickness (when corrected for width, hardness and temperature of the metal being rolled) provides the force required for the stand. Because the force ratio is normalized with respect to a chosen percentage draft, accurate adaptive updating of the process representation can be achieved conveniently by altering only the magnitude curves.

United States Patent Spradlin 1 Jan. 30, 1973 [54l COMPUTER CONTROLLEDROLLING [57] ABSTRACT MILL A computer controlled rolling mill isdescribed [75[ Inventor: Louis W. Spradlin, Scotia, NY

[73] Assignee: General Electric Co.

[22] Filed: Nov. 19,1971

[21] Appl. No.: 200,400

[52] US. Cl ..72/8, 235/15 1.1 [51] i.B21b 37/00 [58] Field of Search..72/7-l0, 16

[56] References Cited UNITED STATES PATENTS R26,996 12/1970 Beadle et al4.72/7 3,574,280 4/1971 ,..72/8 3,592,031 7/1971 Sutton et al. ..72/83,631,697 1/1972 Deramo et al ..72/8 3,641,325 2/1972 Arimura et a1...72/8 X Primary Examiner-Milton S, Mehr Attorney-John .l. Kissane eta1.

wherein the force (or power) model in the computer is stored as dualcurves, ie, (a) shaping curves wherein the ratio of the force requiredfor actual rolling conditions relative to the force required for achosen draft is plotted against elongation, and (b) magnitude curveswherein the force required for the chosen draft is plotted againstinverse output thickness from the mill with each point of the magnitudecurves having an associated stored temperature value. The arithmeticproduce of the force ratio required for a desired elongation and theforce magnitude for a desired output thickness (when corrected for widthhardness and temperature of the metal being rolled) provides the forcerequired for the stand. Because the force ratio is normalized withrespect to a chosen percentage draft. accurate adaptive updating of theprocess representation can be achieved conveniently by altering only themagnitude curves.

16 Claims, 13 Drawing Figures FROM FROM FROM ream o o c 10 c 2.0 c to c10 m 5 To ram MPH 20 vRl PATENTEDJAN 30 I975 SHEEI 3 [IF 9 FORCE WIDTH#f (TONS/INCH) HOUT =4 32 TEMP 3 HouT=2" 18 TEMPZ 24 Howl-=1" 20 TEMP! ICONDITION FOR NORMALIZING 0 1 ELONGATION (Pen UNIT) FORCE/ WIDTH vs.ELONGATION -:22:: l 307.. IZZY-'1 (PER UNIT) I F TEMPZ HouT=+" 1.0 LTEMP 3 HouT-a 30c TemP 30 30 30A L 3 ELONGATION (PER UNIT) FORCE RATIOvs. ELONGATiON (SHAPING cuaves) FORCE oz (TONS/INCH) Z 32 (:wcnas)OUTPUT THlCKNESS FORCE 3070 vs. INVERSE THICKNESS (MAGNITUDE CURVE)SHEEI 3 BF 9 MAGNITUDE cuave FNORM =(HOUT,TEMPR) SUBROUTING PNORM901cm", TENPR) HOUTR HINR ' 42 SHAPING cuRvE FRAT=S(HOUT, HIN) suBRouTmGPRAT= 901001; Hm)

44 5 CALCULATE FORCE (0R POWER) F FRAT FNORM FOR GIVEN ELONGATION P=PRAT PNORM DENORHALIZE FoRcE(oR PoweR) FoRcE=F-w-DR PROPORTIONAL TOWIDTH AND DEFORMATlO RESISTANCE (AND SPEED FORCE (0R POWER) FIOR PASSFIG.3

PAIENTEDJAXSOIBH 3.713.313

SHEET u [If 9 HOUT TENPR MODE C HECK vAumTY |s' HOUT) 0.5" 2400) TEMPR)lsoo FIG. 4

INITIALIZE MODEL QUANTITY lNDEX FOR FORCE (0R POWER) CALCULATE INVERSEER TH\CKNESS HOUT CHOOSE THE TWO STORED POINTS OF THE msmwue cHoosEPOINTS w AND Y CURVE IN THE VICINTY w OF THE INVERSE rmcx- HERE W NEssER CALCUlATE renpsmwne TCrl =\+&- cr1 T -T coeFFlcuim' mumPuERs w WC wER) FOR STORED POlNTS TCMY KCMY Y ea) DENORMALIZE Pom-rs FOR w TCM FTEMPERATURE EFFECT Y TcM F'y II II CALCULATE. INVERSE [GP 2 ER ERyTHICKNESS FRACTION m aa I I INTERPOLATE TO FIND F NORH=FW'+IGF (Fw -FYoeuoamuzeu FORCE (on POWER) FOR mvease P *IGFUW THECKNESS ER MODE SELECTFORCE POWER SHEEI 5 0f 9 0 III 5 i o l on E FIG. 5

y I I ac, new.

ELONGATIOH PAIENIEUJM 30 ms FORCE FOR 30% REDUCT (TONS/INCH) FORCE FORCE3 HOUT HIN MODE CHECK VALIDITY CALCULATE ELG L ELONGATION HOUT LOCATESTORED DATA POINTS ADS'ACENT CAL- CULATED ELONGATION FROM APPROPRIATECURVES FETCH FOUR PoINTs (A,B.c,D) \JHICH BRACKET RATIo VALUE To BECALCULATED CALC U L AT E HORIZONTAL ELONGATION FRACTION I G ELGF EL ELGIELGrl ELG-l FRATI =FRATA ELGF (FRATB-FRATA) FIND FORCE POWER)FRATz=I=RATc+ ELsFQ-RATo-FRATc) RATIos AT DESIRED PRATI PRATA ELGF(PRATBPRATA) E LONGATON PRAT2 =PRATC+ELGF(PRATD PRATQ UT U INTERPOLATE VER'FRAT= FRATI+ (Ma TICALLY BETWEEN THE FoRcE(oR PowER) (FRAT1 FRATI)RATIos TO FIND RATIo I F'OR DESIRED OUTPUT HOUT- HOUT' {30A} THI K PRAT(HOUT (30 B) I-IourfsoA) l (PRATR PRATI} (AssuMING CURVES 30A AND 305BRACKET THE ANSWER. OTHERWISE, usE APPROPRIATE ADJACENT cuRvEs) FIG.6

HOLUT FRAT (on PRAT) CHECK VALIDITY OBTAIN FORCE(OR POWER) DATA TO BEUSED IN CALCULATIONS CALCULATE THICKNESS FRACT HOUT HouT(3oA) RATIoFRACTION FOR VERTICAL INTERPOLATION (Assumme CURVES 30A AND 308 BRACKETTHE ANSWER.

ADJACENT CURVES.)

mom APPROPRIATE CURVES, ra c -I FOUR POINTS (A, B,C,D') WHICH BRACKETFORCE (OR POWER) RATIO CALCULATE RATIO FRACTION FOR use IN RFRAcT= HINTERPOLATION INTERPOLATE BETWEEN ELONGATION POINTS TO D ELQNGATIQN ELG=ELsI+RFRAcT(eI s2-EI eI) CORRESPONDING To THE GIVEN FORCE RATIO ANDTHICKNESS CALCULATE mcomme THICKNESS ELG HOUT HIN FIG.8

OTHERWISE, USE APPROPRIATE PATENTEDJMBO I973 3.713.313

SHEET 8 BF 9 30 B FDRCE FORCE 30 I FRAT 2 FRAT 30A FRAT I ELG] ELG' ELG2ELONGATION FORCE FOR 30% REDUCT. (Toms/I OUTPUT THICKNESS FIG.

PAIENIEIIJMD ma SHEEI 9 [If 9 THIS PASS BETWE V CALCULATE MEASURED MODELFORCE (OR POWER CORRECTED FOR BIAS OFFSET) FOR PASS NORT'IALIZED FORWIDTH. RESISTANCE TO DEFORVIAT|ON,TEIIP- ERATURE AND ELONGATION/FORCE(0R POWER) RATIO (AND SPEED) nEAsuRED MODEL FORCE (OR PDWER 2ER 4 YES ENTHE ENTRY [cALcuLATE INVERSE THICKNESS (ALL PASSES CHECKED J 'vINCREHENT PAss PAss AND THE DELIVERY PAss I YES INDEX SUPPLY INVERSETHICKNESS VALUES FOR REMAINING DumMIED PASSES AND SUPPLY MEASURED MODELFORCE (OR POWER) VALUES BASED ON EXTRAPQLATION CALCULATE INTERIM FORCE(OR POWER) FOR NEW MODEL BASED ON TEMPERATURE OF OLD MODEL [CALCULATEINVERSE THICKNESS PASSES CA LC ULATED {YES CALCULATE TEMPERATURE TERMFOR NEW MODEL NORMALIZE INTERIM FORCE (OR POWEFOTERM OF NEW MODEL TOCORRESPOND TO CALCULATED TEMPERATURE TERM ALL FF'IRIU) I 'DEN-FMRATI(I)'CF TRIU) PNRI-PBIASIU) I Pnnma): DEN-VSLRI (DPMRATIG) (Emu) PNMRI(1)=OEn mm) EMMRI (J) EMMR1(I)= 2 I+ KFTR (TOLDR-TMRT (1)) 1+ KFTR (TMODIUTMRI(I)) I+ KPTR (TOLDR-TM RICD) FIG.lO

COMPUTER CONTROLLED ROLLING MILL This invention relates to a method andapparatus for rolling metal and, in particular, to a computer controlledrolling mill wherein the on-line mathematical models for force and/orpower prediction are stored within the computer as both shaping data andmagnitude data representations with the force and/or power required forthe mill being calculated as an arithmetic product of data derived fromthe stored representations. This particular form for the on-line processrepresentation permits accurate prediction of rolling parameters for awide range of conditions, while still permitting convenient updating ofthe process model by adaptive feedback.

In computer controlled rolling mills, it is customary to determinepredicted rolling parameters, such as rolling force or power, byreference to mathematical models stored within a computer by equationsor coordinates defining families of curves representing the relationshipbetween the rolling parameters and physical characteristics of metalbeing rolled, e.g., inverse output thickness, elongation, et cetera.After proper adjustment, these models may be considered to accuratelyrepresent the rolling process for the average operating condition, withvariations from this average operating condition being taken intoaccount for prediction of rolling parameters for a particular case. Theaccuracy of the predictions for each particular case will depend on theamount of variation from average operating conditions and how accuratelyvariations from the average operating conditions are taken into account,the latter being a function of the form of the stored processrepresentation. Depending on the form of the process representation,weaknesses may exist regarding the ability of the process representationto be used to accurately predict rolling parameters for a wide range ofrolling conditions, and accurate updating of the process model byadaptive feedback may be difficult.

It is therefore an object of this invention to provide a method ofrolling metal utilizing novel stored data to determine rollingparameters.

It is also an object of this invention to provide an accurate method ofrolling metal in one or more passes wherein critical rolling parametersare predicted utilizing stored data representing both shaping andmagnitude curves.

It is a further object of this invention to provide a computercontrolled rolling mill wherein the accuracy of prediction of criticalrolling parameters is maintained notwithstanding wide variations inoperating conditions.

It is a still further object of this invention to provide a method ofrolling metal wherein precise adaptive feedback of stored informationcan be accomplished by adaptively updating only one of two curvesrepresenting the parameter being updated.

These and other objects of this invention generally are achieved bystoring the force (or power) models as dual curves, i.e., (a) a shapingcurve depicting the ratio between actual force and force for a chosenpercentage draft against a function of the deformation of the rolledmetal, e.g., elongation or per unit draft, and (b) a magnitude curvewherein the force for the chosen percentage draft is plotted as afunction of the thickness of the rolled metal, e.g., inverse outputthickness. The force for rolling then is determined by accessing each ofthe curves to determine, for example, (a) the force ratio valueassociated with the amount of deformation to be achieved and (b) theforce magnitude value associated with the thickness of the rolled metal,and these values are multiplied to provide the force required for themill during rolling. Typically, the ratio curves are plotted againstelongation or per unit draft while the magnitude curves define force (orpower) against workpiece thickness or inverse output thickness. Inconventional fashion, the force (or power) thus determined from the dualcurves is adjusted for such factors as workpiece width and hardness (andmill speed) prior to utilization in the mill.

Although the invention is described with particularity in the appendedclaims, a more complete understanding of the invention may be obtainedby the following detailed description taken in conjunction with theaccompanying drawings wherein:

FIG. 1 is an isometric view of a computer controlled roughing mill inaccordance with this invention,

FIG. 2 is a pictorial illustration showing curves stored within thecomputer model and the source of their origin,

FIG. 3 is a flow chart illustrating a method of determining force orpower in accordance with this invention,

FIG. 4 is a How chart illustrating the force and power magnitude curvesubroutines of FIG. 3,

FIG. 5 is an enlarged view showing a portion of the curve depicted inFIG. 2c,

FIG. 6 is a flow chart showing the force and power shaping curvesubroutines of FIG. 3,

FIG. 7 is an enlarged view showing a portion of the curves depicted inFIG. 2b,

FIG. 8 is a flow chart illustrating a method of determining inputthickness utilizing the curves of FIG. 2,

FIG. 9 is an enlarged view showing a portion of the curves depicted inFIG. 2b,

FIG. 10 is a flow chart depicting a technique for adaptively updatingthe magnitude curve of FIG. 2c, and

FIG. II are curves illustrating the method of adaptively updating thecurve of FIG. 20.

A roughing mill 10 in accordance with this invention is illustrated inFIG. 1 and generally includes a plurality of tandem rolling standsRSI-RS3 for incrementally reducing the thickness of bars 81-83 as thebars pass sequentially from upstream stand RS1 to downstream stand RS3.It will be appreciated that an actual tandem roughing mill normally ischaracterized by more than three rolling stands and rolling stands RSI,R82 and RS3 therefore should be considered to represent the first stand,an intermediate stand and the last stand of such roughing mills, e.g.,the first, fourth and seventh stands, respectively, of a seven-standroughing mill. In conventional fashion, each rolling stand is providedwith a pair of confronting work rolls R1 and R1 with the work rolls ateach stand typically being driven by synchronous motors DMI-DM3,respectively, to rotate the rolls at a predetermined speed. A load cellLCl-LC3 underlies the work rolls at each stand to measure the force atthe stands although the load cells also could be situated at any othersuitable position for measuring rolling force, e.g., overlying the workrolls. The amount of reduction of the metal being rolled is determinedby the separation between the work rolls which separation is establishedby screwdowns SDI-SDI! driven by screwdown position drives SDPDl-SDPD3,respectively. A screwdown position indicator ESPll-ESP13 also isprovided at each stand to measure the position of the screwdowns attheir respective stands.

Each stand also has a pair of vertically disposed rollers VRl-VR3 drivenby motors VDM1-VDM3 to reduce the width of each bar, as desired. Anedger adjust mechanism EAM1EAM3 driven by edger screw position drivesESPDl-ESPD3 serves to establish the reduction of bar width while edgerscrew position indicators VSDPll-VSDP13 provide output signalsindicative of the position of the width controlling screws at eachstand. The output signals from all the screw position indicators and allthe load cells along the mill are fed as inputs to computer C20 and thecomputer generates control signals for the screwdown position drives toestablish the draft taken by each set of confronting rolls (as will bemore fully explained hereinafter).

Drive motors DM 1-DM3 generally are fixed speed synchronous motors withthe span between rolling stands being slightly in excess of the lengthof each bar between the rolling stands. The current and voltage appliedto each of the drive motors are sensed by current sensors Al-A3 andvoltage sensors Vl-V3, respectively, and fed to computer C20 to indicatethe power supplied from computer C20 to the drive motors at each stand.Alternatively, a power sensor utilizing these inputs can supply a signalto the computer proportional to the measured motor power. Although notshown for the purpose of clarity, it will be appreciated that adjustablespeed motors could be employed in conjunction with the constant speeddrive motors DM l-DM3 to reduce the total span required for the roughingmill. Adjustment of the mass flow between stands driven by the constantspeed and adjustable speed motors then would be accomplished under thecontrol of computer C20 in conventional fashion using techniques such asare taught in US. Pat. No. 3,170,344, issued to R.E. Marrs and assignedto the assignee of the present invention. In similar fashion, thevoltage and current inputs to drive motors VDMl-VDM3 can be monitoredand fed to computer C20 by suitable measuring equipment (not shown).

Computer C20 is a conventional process control digital computer andtypically may have one or two central processor units with a core memoryof about 400,000 bits and a working drum memory for an additional l to 3million bits of information. The computer normally includes a cardreader 22 to input information relative to the order being processed,e.g., metallurgical composition of the bars, desired output gage, etc.,while process information supplied to, or calculated by, the computermay be visually recorded by a typewriter or a line printer 24. Computershaving these characteristics are commercially available and can beobtained from the General Electric Company under the Trademark GEPAC4010 and GEPAC 4020.

Process control information fed to the computer typically would includethe temperature of the steel being rolled (as measured by pyrometer Pdisposed at a suitable location along the length of the rolling mill). Ameasured indication of the incoming thickness of each bar also desirablyis fed to computer C20. This may be done by any suitable device for suchpurpose, e.g., a vertically scanning light source L having an elongatedlight detector D for observing interruption of the light beam by thebars. The incoming thickness of a bar at a given stand (other than forthe first reduction) generally can be estimated by the computer to ahigh degree of accuracy from the observed gagemeter thickness of the barat a previous stand.

During operation of the mill, a drafting schedule may be chosen whereinthe final stands, e.g., RS3, effect maximum draft in the bars, with theupstream stands, e.g., RSI, producing little or no draft in the bars inorder to conserve the heat content of the bars. ln setting up suchschedule, the downstream stand draft generally is determined inconventional fashion by the more stringent of such constraining limitsas the maximum draft desired for the stand, the force limit imposed bythe mechanical characteristics of the stand, the power limit of thedrive motor and the permissible bite angle at the stand. Maximum draftthen is taken at the final stand, e.g., RS3, and similarly for each ofthe successive upstream stands, to determine the maximum permissiblereduction by the roughing mill. When the incoming bar to be rolled has athickness less than the calculated maximum thickness capable of beingrolled for the given conditions (width, temperature, and hardness of theworkpiece), the upstream stands, e.g., RS1, are assigned a lesser draftby the computer drafting schedule calculation while the reductions forthe downstream stands, e.g., RS3, are maintained at their previouslycalculated maximum permissible values. The desired screwdown positions(as determined in conventional fashion from the desired output thicknessfrom the stand and the known spring of the stand for the force requiredto produce the desired draft) then are established by the computer. Whenoperating on such a rolling schedule, the draft taken at a roughingstand, particularly the upstream stands, may vary considerably as afunction of slab dimensions and defined limits. It will be appreciated,however, that the metal rolling method of this invention can be utilizedwith any conventional rolling schedule draft distribution calculationstrategy which utilizes a mathematically or empirically determinedrelationship of force per unit workpiece width or power per unitworkpiece width as a function of workpiece deformation, e.g., elongationor per unit draft.

in accordance with this invention, the mathematical model for rollingforce is stored within the calculated model of computer C20 as (a)shaping curves, e.g., the ratio of force for actual rolling conditionsto force for a chosen draft as plotted against elongation (illustratedin FIG. 2b for a chosen 30 percent draft) and (b) magnitude curves,wherein force for the chosen draft is plotted against the reciprocal ofoutput thickness (as shown in FIG. 2c). Each of the shaping curves arenormalized, i.e., intersect, at the chosen percentage of draft, and areconsidered to represent the non-linear characteristics of rolling forceas a function of the amount of reduction taken. The shaping curves ofFIG. 2b therefore can be considered to be stable during rolling withonly the magnitude curves of FIG. 2c possibly requiring adjustment inorder to provide a means of adaptive feedback for the processrepresentation.

The shaping and magnitude curves of FIGS. 2b and 2c may be derived fromthe overall process relationship shown in FIG. 24, wherein the indicatedpoint for normalization corresponds to a 30 percent draft condition. Theelongation corresponding to the chosen per unit draft is calculated fromthe known relationships:

p.u. draft Hin Hout/Hin wherein p.u. draft is the per unit draft, Hin isthe input thickness of the bar, and Hout is the output thickness of thebar, and

ELG Hin/Hout wherein ELG is elongation.

At the elongation obtained from the foregoing equations, i.e., a 1.43elongation for the chosen 30 percent draft, the shaping curves have aunitary ratio of actual force per unit width to force per unit width forthe 30 percent draft condition, thereby providing the focal point F forthe curves of FIG. 2b. The overall process relationship force curves ofFIG. 20 then are entered at a value of 1.43 for elongation to determinethe corresponding values on magnitude curve 2c for the diverse outputthicknesses. For other elongations, the product of curves 2b and 2cprovides the actual force value determined from FIG. 2a. Thus, for anelongation of 1.43 and a force ratio designated as 1.0, a force of 24tons/inch is indicated by curve 32 as being required to reduce a bar (atthe temperature of the curve) to an output thickness of 2 inches. This 2inch output thickness corresponds to an inverse output thickness of 0.5inches, i.e., l/(2.0 inches), and forms a point W for magnitude curve34. Similarly, points X, Y and Z on magnitude curve 34 (corresponding toinverse output thickness of 1, 4 and 8 inches, respectively), aredetermined by observing on curves 32A, 32B and 32C, respectively, theforces (20 tons, 28 tons and 32 tons) required to effect a 1.43elongation in bars having output gages of l, 4 and 8 inches,respectively. Each point on curve 32 then is divided by the force, i.e.,24 tons, at the chosen per unit elongation to obtain curve 30 of FIG.2b. Similarly, the force at each point on curve 32A is divided by 20tons (i.e., the force required for a 1.43 elongation) to obtain curve30A of FIG. 2b, while curves 30B and 30C are obtained by dividing curves32B and 32C by 28 and 32 tons, respectively, i.e., the force per unitwidth for the curves at the chosen elongation. Because each of shapingcurves 30-30C are brought to a force ratio of 1.0 at the chosen per unitdraft in determining the configuration of the shaping curves, all theshaping curves necessarily intersect at the elongation corresponding tothe chosen per unit draft. Each of shaping curves 30, 30A, 30B and 30Cthen are stored within computer C20 by coordinates representing pointsalong each curve. Similarly, magnitude curve 34 is stored by the forcemagnitude, inverse thickness, and temperature corresponding to points W,X, Y and Z. It will be appreciated that in actual practice, each shapingand magnitude curve would typically be defined by approximately six topoints.

To determine predicted rolling force of roughing mill 10, the shapingand magnitude curves of FIGS. 2b and 2c are accessed to determine forceratio and force values for a desired elongation and inverse outputthickness, respectively, whereafter the force ratio and force values aremultiplied to produce predicted rolling force as illustrated in the flowchart of FIG. 3. Thus, the magnitude curve of FIG. 2c is enteredutilizing magnitude curve subroutine 40 to obtain normalized force,i.e., the force required to produce a 30 percent draft for the desiredoutput thickness at the known temperature, and the shaping curves ofFIG. 2b are entered utilizing shaping curve subroutine 42 to obtain theforce ratio, i.e., the ratio of actual force to force for the chosendraft, required to produce the desired elongation. The normalized forceand force ratio then are multiplied in multiplier circuit 44 to obtain acalculated force for a given elongation and this calculated force isadjusted by empirically determined multiplication factors proportionalto the known width and resistance to deformation of the bar to providethe predicted mill rolling force.

A magnitude curve subroutine suitable for determining the value ofnormalized force is illustrated in the flow chart of FIG. 4. The inputdata required for the subroutine is the desired output thickness HOUTand the incoming temperature TEMPR of the bar (as esti mated by thecomputer utilizing either the known temperature of previously rolledbars, as measured by pyrometer P, or the temperature customarilyproduced in the bars during the most recent previous heats in thefurnace (not shown) from which the bars enter the roughing mill).Because this subroutine can be employed both to determine eithernormalized force or normalized power dependent upon the operative modeof the subroutine, a mode indication normally is also supplied as partof the subroutine input data. The computer then checks the validity ofthe input information by observing that the desired output thickness iswithin the limits of the rolling mill, e.g., is between 0.5 and 15inches, and that the temperature of the incoming bars is within a rangesuitable for rolling, e.g., between 1,500 F and 2,400 F. With thesubroutine in a force mode, the model index is initialized for force andthe force coefficients of curve 34 are utilized by the subroutine. Thecomputer calculates the inverse thickness ER of the bar by taking thereciprocal of the known desired output thickness Hout whereafter thecomputer chooses the two stored points of magnitude curve 34 straddling(or otherwise nearest) the inverse thickness ER in question, e.g., 0.5inch corresponding to point W and 0.25 inch" corresponding to point Y(see enlarged FIG. 5). The temperature coefficient multiplier TCM forpoint W then is calculated in accordance with the formula:

wherein K CM is a temperature coefficient factor representing thepartial derivative of per unit rollin g force with respect totemperature of the bar,

7' is the temperature of the metal being rolled, and

T is the temperature value associated with point W. The force at point Wthen is denormalized for temperature effect to obtain point W inaccordance with the fonnula:

wherein W is the model quantity corrected for temperature,

TCM is the temperature coefficient multiplier, and

F is the force at point W before interpolation.

After the temperature coefficient multiplier for point Y is calculatedand the force at point Y is denormalized for temperature effect toobtain point Y (using the previously explained technique for obtainingpoint W), the inverse thickness fraction [CF to be used in interpolationis determined in accordance with the formula:

IGF= ER ER /ER ERy wherein ER is the inverse output thickness in point,

ER is the smaller of the two stored inverse output thickness pointsstraddling the inverse output thickness in point, i.e., 0.25 in FIG. 5,and

ER is the larger of the two stored inverse output thickness pointsstraddling the inverse output thickness in point, i.e., 0.5 in FIG. 5.The force (or power, dependent on mode) FNORM denormalized for thetemperature and inverse output thickness in question then is determinedby interpolation in accordance with the formula:

wherein FNORM is the interpolated denormalized force for an inverseoutput thickness ER,

F is the force for point W,

IGF is the inverse thickness fraction, and

Fy' is the force for point 1''.

This normalized force then is checked against force limits before beingemployed to calculate the actual rolling force in accordance with FIG.3.

The operation of the subroutine of FIG. 4 can be understood from thefollowing specific calculations of normalized force required to producean output thickness of 3 inches in a bar having a temperature of 2,000F. The computer initially checks the desired output thickness andtemperature against known limits whereupon the inverse output thicknessis calculated to be 0.333 inches", i.e., the reciprocal of the desiredoutput thickness. The computer then locates this inverse thickness asbeing between stored points W and Y having inverse output thickness of0.5 inch" and 0.25 inch", respectively. The temperature coefficientmultiplier for point W next is calculated by taking the difference intemperatures between the stored point and the temperature of the bar,e.g., 2,l F 2,000 F, and multiplying the answer by a temperaturecoefficient factor (KCM) of, for example, l0" p.u./F, i.e., theempirically determined partial derivative of per unit rolling force withrespect to temperature of the bar, to arrive at the per unit forcecorrection, e.g., 0.1, required because of the temperature differencebetween the temperature corresponding to stored point W and thetemperature of the bar. The force correction is added to 1.0 to obtainthe temperature coefficient multiplier, i.e., 1.1., and the force atpoint W, e.g., 24 tons/inch, is multiplied by the temperaturecoefficient multiplier to obtain point W, i.e., 26.4 tons/inch.Similarly, point Y would be corrected for temperature differencesbetween stored point Y and the bar tem perature to obtain point Y. Aninterpolation fraction equal to D,/D,, i.e., the quotient of (ER 0.25)and (0.5 0.25 illustrated in FIG. 5 is calculated and the value oftemperature normalized force FNORM for the desired elongation isdetermined from curve Y W A subroutine suitable for finding the forceratio FRAT to be employed in the flow chart of FIG. 3 is illustrated inFIG. 6. The input information to the computer for the subroutinegenerally would include the entry thickness, Hin, and the desired exitthickness, Hout, of the bar as well as the desired mode of operation,i.e., a force mode, for the subroutine. After the routine has checkedthe validity of the input information to determine that the exitthickness is within a prescribed tolerance, e.g., between 0.5" and15.0", two curves of FIG. 2b to be employed in determining the forceratio are chosen by identification of those curves bracketing (orotherwise nearest) the desired exit thickness. Thus, for an exitthickness of 1.5 inches, curves 30 and 30A would be employed for thesubroutine while an exit thickness of 2.5 inches would require theutilization of curves 30A and 308 in the subroutine. The entry thicknessthen is compared to the exit thickness by the computer to check thevalidity of the information, i.e., that the entry thickness is greaterthan the exit thickness, and the elongation ELG is calculated as thequotient of the entry thickness and the exit thickness. The calculatedelongation then is located on the stored ratio curves, i.e., as being avalue between stored elongation points ELG] and ELG2 along the curves,and the coordinates of the four stored points A, B, C and D (illustratedin FIG. 7) bracketing the ratio value are obtained. The elongationfraction ELGF TO BE USED FOR HORIZONTAL INTERPOLATION THEN lS CALCULATEDFROM THE FORMULA:

wherein 7 ELG is the desired elongation for the bar,

ELG is the elongation at the stored data point,i.e., point A, having anelongation immediately below the desired elongation, and

ELG; is the elongation at the stored data point, i.e., point 8, havingan elongation immediately above the desired elongation.

Assuming an output thickness between 2 inches and 4 inches, the forceratios FRATl and FRAT2 at elongation ELG then are determined from curves30A and 3013 using the formulas:

FRATl FRATA ELFG-(FRATB FRATA) and FRATZ FRATC ELGF-(FRATD FRATC)wherein FRATl is the force ratio at point X on curve 30A, FRATA is theforce ratio at point A on curve 30A, FLGF is the elongation fraction,FRATB is the force ratio at point B on curve 30A, FRATZ is the forceratio at point Y on curve 308, FRATC is the force ratio at point C oncurve 308, and

FRATD is the force ratio at point D on curve 308.

After determining the force ratios at points X and Y, verticalinterpolation is made to find the force ratio for the thickness inquestion in accordance with the formula:

FEAT: FRATl HOUT HOUT(30A) HOUT(30B) -HUT(30A (FRATz FEAT) wherein:

FRAT is the force ratio for the desired output thickness,

FRATl is the force ratio at point X on curve 30A,

HOUT is desired output thickness,

HOUT(30A) is the output thickness corresponding to curve 30A,

HOUT(30B) is the output thickness of curve 308, and

FRAT2 is the force ratio at point Y on curve 308.

Knowing the normal force as calculated by the mag nitude curvesubroutine of FIG. 4 and the force ratio as calculated by the shapingcurve subroutine of FIG. 6, the force desired for rolling is predictedby multiplying these two quantities to obtain the force product as shownin FIG. 3. Before use of the force product for adjustment of thescrewdowns, however, the force product normally is adjusted bymultiplication factors corresponding to the resistance to deformation ofthe metal being rolled (dependent on the metallurgy of the rolled bars)and the width of the bars (as determined by the setting of verticalrollers VRl-VRS). Information concerning the metallurgy and desiredwidth are provided for the computer C by the operator at the initiationof rolling and the computer chooses theoretically or empiricallydetermined multiplication factors to be used in the force calculationsfrom stored information associated with these inputs.

When curves 2b are the ratio of actual power to power required for 30percent draft plotted against elongation and curve 2c defines therelationship between power required for 30 percent draft and inverseoutput thickness, the rolling power for each stand can be calculatedutilizing the routines illustrated in FIGS. 3, 4 and 6. In theseFigures, the required power routines are shown in brackets whendiffering from the heretofore explained force routines. To determinerolling power, the subroutine of FIG. 4 would be placed in a power modeby the calling sequence and the stored power curve coefficients (insteadof the force curve coefficients) would be utilized by the subroutine.The subroutine otherwise functions identically to the previouslydescribed operation of the subroutine in the force mode. The output fromthe subroutine, however, is normalized power which is checked againstpower limits before using the normalized power for subsequentcalculations. Similarly, the ratio curve subroutine of FIG. 6 isemployed to determine power ratio by indexing data corresponding to thepower ratio curves (instead of the force ratio curves), as a function ofthe mode indicator. The subroutine then functions identically to thepreviously described operation of the subroutine in the force mode withthe ratio provided by the subroutine being a power ratio rather than aforce ratio. The power ratio and the normalized power as determined bythe subroutines of FIGS. 6 and 4, respectively, then are multiplied toprovide the rolling power for the mill and this rolling power isadjusted by empirically determined multiplication factors dependent uponthe relative resistance to deformation and width of the bars and thespeed of stands RSlRS3 before being used to predict the power requiredby the drive motors forming the mill for the given rolling conditions.

Although desirably the curves of FIG. 2b are employed to determine force(or rolling power) ratio from known entry and exit thicknesses for thebars, the curves of FIG. 2b also can be accessed in opposite fashion todetermine the required entry thickness of the bars knowing the specifiedexit thickness HOUT and the specified rolling force (or power) ratio byutilization of the routine shown in FIG. 8. The specified exit thicknessprovided for the subroutine is checked for validity and the force ratiocurves of FIG. 2b having exit thicknesses immediately above and below(or otherwise nearest) the specified exit thickness are chosen for thecalculations, e.g., curves 30A and 30B of FIG. 9. The stored force ratiodata for these curves then is accessed by the computer and a thicknessratio fraction FRACT for use in vertical interpolation is determined inaccordance with the formula:

FRACT=HOUT(30B) HOUT(30A) wherein HOUT is the specified exit thicknessfor the bar in inches,

HOUT(30A) is the exit thickness of the stored data curve, i.e., curve30A, immediately below the specified exit thickness, and

HOUT(30B) is the exit thickness of the stored data curve, i.e., curve308, immediately above the specified exit thickness. Knowing thethickness ratio fraction and the specified force ratio, a search isinitiated to determine the coordinates of the four stored force ratiodata points A, B, C and D encompassing the specified force ratio FRAT.In searching, the value of the force ratio FRAT initially is compared toL0 to determine the stored data points which need be considered, i.e.,data points corresponding to an elongation between 0. and 1.43 or datapoints corresponding to an elongation above 1.43. The computer thenchooses an elongation ELG2 on curve 30A having a corresponding forceratio immediately below the specified force ratio FRAT and the forceratio FRATZ at the chosen elongation ELGZ is calculated using theformula:

FRAT2= FRATB' FRACT-(FRATD' FRATB') wherein FRATB' is the force ratio ofpoint B of curve 30A of FIG. 9 corresponding to an elongation ELGZ,

FRACT is the thickness ratio fraction, and

FRA'I'D' is the force ratio at point D of curve 308 corresponding to anelongation ELGZ. This calculated force ratio then is compared to thespecified force ratio and if the specified ratio is more than thecalculated ratio, the force ratio at the immediately lower storedelongation point ELGI is calculated in an identical manner to findFRATI. If the calculated force ratio FRATI is lower than the specifiedforce ratio, FRAT, then points A, B, C and D are selected as thecoordinates bracketing FRAT. Should the calculated force ratio atelongation ELGI be larger than FRA T, the computer would successivelycalculate the force ratio at each succeedingly lower elongation toselect the bracketing coordinates for the specified force ratio F RA T.Knowing the bracketing coordinates, the ratio fraction RF RACT used forinterpolation is calculated from the formula:

RFRACT=(FRAT- FRATl/FRATZ FRATI) wherein FRAT is the specified forceratio (for the required elongation),

FRAT] is the calculated force ratio at point X of curve X'Y', and

FRAT2 is the calculated force ratio at point Y of curve X'Y'. Therequired elongation ELG associated with the specified force ratio FRATthen is determined by interpolating between elongation points ELGl andELGZ and utilizing the formula:

ELG'=ELG1+ RFRACT (ELGZ-ELGI) wherein 161 is the elongation at point Xof curve XY', ELGZ is the elongationat point Y of curve X'Y, and

RF RACT is the ratio fraction. Knowing the required elongation and thespecified exit thickness, the required thickness MN is calculated as theproduct of these quantities, i.e.,

HIN ELG HOUT wherein ELG' is the calculated required elongationcorresponding to the specified force ratio FRAT, and

HOUT is the specified exit thickness of the bar.

When the ratio curves and the magnitude curves are power curves, thesubroutine of FIG. 8 also can be employed (in the manner described withreference to the force ratio curves) to determine entry thickness of thebars. The output thickness and power ratio would be provided for thesubroutine and the data utilized during calculations would be powerratio curve data rather than force ratio curve data stored within thecomputer memory.

One of the major advantages of dual force (or power) curves inaccordance with this invention resides in the fact that accurate on-lineadaptive feedback can be achieved conveniently by updating only themagnitude curve of FIG. 20 in response to measured deviations betweenactual and anticipated force (or power) levels in the mill. One routinefor achieving the desired adaptive feedback is illustrated in FIG. 10wherein both the force and power feedbacks are depicted on the sameroutine. in a force feedback mode, a measured model" magnitude curve iscalculated, based on measured values. As will be seen, on-line feedbackon the force model consists of modifying the force magnitude curve (in avector sense) partially toward correspondence with the measured model"curve. The measured model force is calculated based on the measuredforce, normalized for width, hardness, temperature and elongation inaccordance with the fonn ula:

wherein FMMRKI) is the measured model force (magnitude) value for themeasured rolling conditions during pass (I), but corresponding to actualmodel temperature,

FMRKI) is the measured force for pass (I),

DEN is a calculated normalizing factor, the product of strip width andthe hardness multiplier for the type of product rolled,

FMRATH) is the measured force ratio determined from the elongationassociated with the measured input and output thicknesses for pass (I),and

CFTRIU) is a force temperature coefficient multiplier corresponding tothe difference between the actual model temperature and the estimatedtemperature for pass (l).

When the measured model force is zero (a dummied pass condition) and thedummied pass number is identified as between the delivery pass and theentry pass, the measured model inverse thickness EM MR1) (a suppliedvalue) is calculated from the formula:

EMMRI EM.\IRI (J)-i2-E.\I.\IRI (K) wherein EMMRI (.I) is the measuredmodel inverse thickness for the first active pass upstream of the passin question,

EMMRI (K) is the measured model inverse thickness for the first activepass downstream of the pass in question. This logic is included in orderto provide measured model values for all passes, including possibledummied passes. Measured model values for dummied passes at either endof the mill (if any) are provided by extrapolation.

The measured model force calculation then is repeated for all passes.

Measured model force values for dummied passes (if any) then arecalculated by interpolation between adjacent values for active passes.The interim force (or power) terms for the new model are calculated(based on temperature of the old model) using the formula:

FMODKI) FMODKI) KFBR (FMMRl(l)- FMODKI) wherein FMODKI) is the force(magnitude) model term for p KFBR is the adaptive feedback gaincorresponding to the chosen fraction of the difl'erence between measuredforce and stored force to be utilized in correcting the stored forcerepresentation,

FMMRHI) is the measured model (force) value for pass (I). The inversethickness for the new model next is detennined using the formula:

EMODIU) EMODIU) KFBR (EMMRl(l)- EMODl(l)) wherein EMODIU) is the inversethickness term for the force model for pass (I),

K FBR is the adaptive feedback gain for updating the force term, and

EMMRIU) is the measured model inverse thickness for pass (1). After theinverse thickness for each pass is calculated, the temperature value ofthe old model is temporarily stored and the temperature term for the newmodel is calculated in accordance with the formula:

TMODKI) TMODI(I)+KTFBR (TMRI(I)- TMODl(l)) G) [11 KFTR-(TOLDRTMRI(I))+KFTR-(TMODI (I) TMRI (1)) wherein PMODI(I) is the force (magnitude)model term for P KFTR is the temperature coefficient factor representingthe partial derivative of per unit rolling force with respect totemperature of the bar,

TOLDR is the model temperature value for this pass prior to updating,

TMRI(I) is the measured model temperature for pass TMODI(I) is the modeltemperature value for this pass, after updating.

The adaptive force feedback is illustrated graphically in FIG. 11wherein magnitude curve 34C is stored within the computer by points50-54 corresponding to the average output thickness from each stand (orpass). The measured model points actually determined from measurementsat each stand (by the load cells LC l-LC3 and screwdown positionindicators ESPll-ESP13 during a pass of bars B1-B3 through mill areidentified by reference numerals 60-64 and form curve 68. The computerthen calculates a weighted average of corresponding points along curves34C and 68, i.e., point 50 is averaged with point 60, point 51 isaveraged with point 61, etc., to obtain average points 70-74, theupdated force model (magnitude) curve. This new curve is employed in themodel calculations for the force setting for the next bar passingthrough the mill. Because a great deal of credibility can be given toexisting model data points (i.e., points 50-54, already stored withinthe computer, which are based upon a number of previous passes) ascompared with the measured model data points (i.e., points 60-64,measured during a single pass) the average between corresponding pointsdesirably is weighted to shift the measured model data points only asmall fraction, e.g., one-fourth, of the span between the stored andmeasured data points. This weighting is accomplished by the selectedvalue of the feedback gains KFBR and KTFBR.

When the power magnitude curves are to be updated by adaptive feedback,the measured model power for the pass is calculated, based on themeasured motor power corrected for power bias offset (to obtain rollingpower) and normalized for width, hardness, temperature, elongation/powerration and speed in accordance with the formula:

wherein PMMRIU) is the measured model power (magnitude) value,corresponding to the measured rolling conditions for pass (I), butcorresponding to actual model temperature,

PMRI( I) is the measured motor powers for pass I,

PBIASKI) is the motor power bias value for stand (I), i.e., the motorpower required to overcome windage and friction when there is no steelbeing rolled,

DEN is calculated normalizing factor, the product of strip width and thehardness multiplier for the type of product rolled,

VSLRI(I) is the strip speed out of pass (I),

PMRATKI) is the measured power ratio determined from the elongationassociated with the measured input and output thicknesses for pass (I),and

CP'I'RIU) is Ppower temperature multiplier, based on the actual modeltemperature and the estimated temperature for pass (I). The measuredmodel power calculation then is repeated for all passes and dummiedvalues are supplied before interim power terms for the new model arecalculated (based on temperature of the old model) using the formula:

PMODI(I) PMODI(I) KFBR (PMMRI(I)- PMODI(I)) wherein PMODI(I) PMODI(I) 1KPTR- (TOLDR TMRI(I)) 1+ KPTR- (TMODI (I) TMRI (1)) in a manner similarto that described for the corresponding force (magnitude) model terms.This new power term then is employed in the model calculations topredict the rolling power in the mill for the next bar passingtherethrough.

While a specific embodiment of this invention as used in a tandemroughing mill has been described, it will be obvious that stored shapingand magnitude curves also can be employed in substantially identicalfashion to control a finishing mill or a single-stand reversing hot millwithout departing from the scope of this invention as described in theappended claims.

What I claim as new and desire to secure by Letters Patent of the UnitedStates is:

1. In a method of reducing the thickness of metal by rolling the metalbetween at least one set of rollers wherein rolling parameters for arolling pass are determined in association with a digital computersystem by access to stored information representing the variation ofsaid rolling parameters as a function of diverse metal characteristics,the improvement comprising storing the magnitude of a rolling parameterselected from the group consisting of power and force as a function ofthe thickness of the metal for a chosen per unit draft taken by saidrollers, storing the ratio of said selected parameter for an actualreduction to said selected parameter for the chosen per unit draft as afunction of the deformation of the rolled metal, determining the valueof said parameter at the chosen per unit draft for a desired outputthickness and the value of said parameter ratio for a desireddeformation and setting said parameter for the succeeding rolling passat the arithmetic product of said determined values.

2. A method of reducing the thickness of metal according to claim 1wherein said selected parameter is force, said force being stored as afunction of inverse output thickness for an associated temperature valueand said force ratio being stored as a function of the elongation of therolled metal.

3. A method of reducing the thickness of metal according to claim 2further including modifying the arithmetic product of force at thechosen per unit draft and temperature for a desired inverse outputthickness and force ratio for a desired elongation by factorsproportional to the width, hardness and estimated temperature of themetal before setting the force for the succeeding rolling pass.

4. A method of reducing the thickness of metal according to claim 1wherein said selected parameter is power, said power being stored as afunction of inverse output thickness for an associated temperature valueand said power ratio being stored as a function of the elongation of therolled metal.

5. A method of reducing the thickness of metal according to claim 4further including modifying the arithmetic product of said power ratioand said power for a chosen per unit draft and temperature by factorsproportional to the width, hardness, estimated temperature and speed ofthe mill before setting the power for the succeeding rolling pass.

6. In a method of reducing the thickness of metal by rolling the metalbetween at least one set of rollers wherein predicted rolling parametersfor a pass of the metal through the rollers are determined inassociation with a digital computer system by access of stored familiesof functions defining relationships between various rolling parametersas functions of metal characteristics, the improvement comprisingdefining a rolling parameter selected from the group consisting of powerand force by a first family of functions describing the ratio of thevalue of the selected parameter for actually contemplated rollingconditions to the value of the selected parameter for a chosen per unitdraft as a function of metal deformation for diverse output thicknesses,said family of functions being characterized by a common intersection atthe chosen per unit draft, defining said selected parameter as afunction of the magnitude of said selected parameter for said chosen perunit draft against the thickness of the metal from the stand for variousassociated temperatures, accessing said stored functions to determinethe magnitude of said selected parameter at the chosen per unit draftfor a desired output thickness and the ratio of the selected parameterfor a desired deformation, and setting the selected parameter for therolling pass at the arithmetic product of said magnitude and said ratioas determined from said functions.

7. A method of reducing the thickness of metal according to claim 6further including measuring the actual parameter at the stand duringrolling and adaptively updating only the stored curve defining themagnitude of said parameter for the chosen per unit draft as a functionof the output thickness, said adaptive updating of said curve being anamount proportional to the difference between the actually measuredparameter and the existing stored functions.

8. A method of reducing the thickness of metal according to claim 7further including modifying the measured parameter by an amountproportional to the width, hardness and temperature of the metal beingrolled, prior to updating of said functions.

9. A method of reducing the thickness of metal according to claim 7wherein said selected parameter is power and further including measuringthe actual power during rolling and adaptively updating only the storedcurve defining the magnitude of power for the chosen per unit draft as afunction of output thickness, said adaptive updating of said magnitudecurve being an amount proportional to the difference between theactually measured parameter and the existing stored functions.

10. A method reducing the thickness of metal according to claim 9further including modifying the measured power by an amount proportionalto the width, hardness and temperature of the metal and speed of thestand prior to updating of said stored functions.

11. A computer controlled method of rolling metal by passing said metalbetween a pair of confronting rollers whereby the incoming thickness,and therefore the amount of reduction, of said metal required to achievea desired magnitude of force for a given output thickness can bepredicted, said method comprising determining the temperature of themetal being rolled, accessing stored data depicting the variation offorce for a predetermined percentage draft as a function of outputthickness to determine the normalized force required to obtain thedesired output thickness, calculating the ratio of the actual force tobe applied at said stand to the normalized force, accessing stored datadepicting the relationship between the ratio of actual force to thenormalized force as a function of a metal deformation factor selectedfrom the group consisting essentially of elongation and per unit draftto determine the quantity of metal deformation produced by thecalculated force ratio and determining the incoming thickness of saidmetal from said metal deformation and said output thickness.

12. A method of rolling metal according to claim 10 further includingadjusting the normalized force by an amount dependent upon the width andhardness of the metal being rolled before calculating said force ratio.

13. A computer controlled method of rolling metal by passing said metalbetween a pair of confronting rollers whereby the incoming thickness,and therefore the amount of reduction, of said metal required to achievea desired magnitude of power for a given output thickness can bepredicted, said method comprising determining the temperature of themetal being rolled, accessing stored data depicting the variation ofpower for a predetermined percentage of draft as a function of outputthickness to determine normalized power required to obtain the desiredoutput thickness, calculating the ratio of the actual power to beapplied at said stand to the normalized power, accessing stored datadepicting the relationship between the ratio of actual power to thenormalized power as a function of a metal deformation factor selectedfrom the group consisting essentially of elongation and per unit draftto determine the quantity of metal deformation produced by thecalculated power ratio and determining incoming thickness of said metalfrom said determined metal deformation and said output thickness.

14. A method of rolling metal according to claim 13 further includingadjusting the normalized power by an amount proportional to the widthand resistance to deformation of the metal being rolled and the speed ofthe stand prior to calculating said power ratio.

15. An automated rolling mill comprising at least one rolling standhaving a pair of confronting rollers, means for adjusting the openingsbetween said rollers, and a computer control system having meansdefining a parameter selected from the group consisting of power andforce by a first family of curves defining the ratio of the parametermagnitude for a chosen per unit draft as a function of elongation, saidfamily of ratio curves being characterized by a common intersection atthe chosen per unit draft, means defining said parameter for a chosenper unit draft as a function of the output thickness of metal passedthrough said stand, means for accessing said stored curves to determineboth the value of the parameter for the chosen per unit draft requiredto produce a desired output thickness in metal passed through saidrollers and the value of said ratio for a given elongation, means forcalculating the arithmetic product for said values as determined fromsaid curves, and means for predicting the selected parameter at saidmill at the arithmetic product of said values.

16. An automated rolling mill according to claim 15 wherein saidselected parameter is force and further including means for measuringthe actual force at said stand during rolling and means for adaptivelyupdating only said means defining force magnitude as a function of theoutput thickness, said adaptive updating being by an amount proportionalto the difference between the representation for actually measuredconditions and the existing representation.

* i i I t

1. In a method of reducing the thickness of metal by rolling the metalbetween at least one set of rollers wherein rolling parameters for arolling pass are determined in association with a digital computersystem by access to stored information representing the variation ofsaid rolling parameters as a function of diverse metal characteristics,the improvement comprising storing the magnitude of a rolling parameterselected from the group consisting of power and force as a function ofthe thickness of the metal for a chosen per unit draft taken by saidrollers, storing the ratio of said selected parameter for an actualreduction to said selected parameter for the chosen per unit draft as afunction of the deformation of the rolled metal, determining the valueof said parameter at the chosen per unit draft for a desired outputthickness and the value of said parameter ratio for a desireddeformation and setting said parameter for the succeeding rolling passat the arithmetic product of said determined values.
 1. In a method ofreducing the thickness of metal by rolling the metal between at leastone set of rollers wherein rolling parameters for a rolling pass aredetermined in association with a digital computer system by access tostored information representing the variation of said rolling parametersas a function of diverse metal characteristics, the improvementcomprising storing the magnitude of a rolling parameter selected fromthe group consisting of power and force as a function of the thicknessof the metal for a chosen per unit draft taken by said rollers, storingthe ratio of said selected parameter for an actual reduction to saidselected parameter for the chosen per unit draft as a function of thedeformation of the rolled metal, determining the value of said parameterat the chosen per unit draft for a desired output thickness and thevalue of said parameter ratio for a desired deformation and setting saidparameter for the succeeding rolling pass at the arithmetic product ofsaid determined values.
 2. A method of reducing the thickness of metalaccording to claim 1 wherein said selected parameter is force, saidforce being stored as a function of inverse output thickness for anassociated temperature value and said force ratio being stored as afunction of the elongation of the rolled metal.
 3. A method of reducingthe thickness of metal according to claim 2 further including modifyingthe arithmetic product of force at the chosen per unit draft andtemperature for a desired inverse output thickness and force ratio for adesired elongation by factors proportional to thE width, hardness andestimated temperature of the metal before setting the force for thesucceeding rolling pass.
 4. A method of reducing the thickness of metalaccording to claim 1 wherein said selected parameter is power, saidpower being stored as a function of inverse output thickness for anassociated temperature value and said power ratio being stored as afunction of the elongation of the rolled metal.
 5. A method of reducingthe thickness of metal according to claim 4 further including modifyingthe arithmetic product of said power ratio and said power for a chosenper unit draft and temperature by factors proportional to the width,hardness, estimated temperature and speed of the mill before setting thepower for the succeeding rolling pass.
 6. In a method of reducing thethickness of metal by rolling the metal between at least one set ofrollers wherein predicted rolling parameters for a pass of the metalthrough the rollers are determined in association with a digitalcomputer system by access of stored families of functions definingrelationships between various rolling parameters as functions of metalcharacteristics, the improvement comprising defining a rolling parameterselected from the group consisting of power and force by a first familyof functions describing the ratio of the value of the selected parameterfor actually contemplated rolling conditions to the value of theselected parameter for a chosen per unit draft as a function of metaldeformation for diverse output thicknesses, said family of functionsbeing characterized by a common intersection at the chosen per unitdraft, defining said selected parameter as a function of the magnitudeof said selected parameter for said chosen per unit draft against thethickness of the metal from the stand for various associatedtemperatures, accessing said stored functions to determine the magnitudeof said selected parameter at the chosen per unit draft for a desiredoutput thickness and the ratio of the selected parameter for a desireddeformation, and setting the selected parameter for the rolling pass atthe arithmetic product of said magnitude and said ratio as determinedfrom said functions.
 7. A method of reducing the thickness of metalaccording to claim 6 further including measuring the actual parameter atthe stand during rolling and adaptively updating only the stored curvedefining the magnitude of said parameter for the chosen per unit draftas a function of the output thickness, said adaptive updating of saidcurve being an amount proportional to the difference between theactually measured parameter and the existing stored functions.
 8. Amethod of reducing the thickness of metal according to claim 7 furtherincluding modifying the measured parameter by an amount proportional tothe width, hardness and temperature of the metal being rolled, prior toupdating of said functions.
 9. A method of reducing the thickness ofmetal according to claim 7 wherein said selected parameter is power andfurther including measuring the actual power during rolling andadaptively updating only the stored curve defining the magnitude ofpower for the chosen per unit draft as a function of output thickness,said adaptive updating of said magnitude curve being an amountproportional to the difference between the actually measured parameterand the existing stored functions.
 10. A method reducing the thicknessof metal according to claim 9 further including modifying the measuredpower by an amount proportional to the width, hardness and temperatureof the metal and speed of the stand prior to updating of said storedfunctions.
 11. A computer controlled method of rolling metal by passingsaid metal between a pair of confronting rollers whereby the incomingthickness, and therefore the amount of reduction, of said metal requiredto achieve a desired magnitude of force for a given output thickness canbe predicted, said method comprising determining the temperature of themetal being rolled, accessing Stored data depicting the variation offorce for a predetermined percentage draft as a function of outputthickness to determine the normalized force required to obtain thedesired output thickness, calculating the ratio of the actual force tobe applied at said stand to the normalized force, accessing stored datadepicting the relationship between the ratio of actual force to thenormalized force as a function of a metal deformation factor selectedfrom the group consisting essentially of elongation and per unit draftto determine the quantity of metal deformation produced by thecalculated force ratio and determining the incoming thickness of saidmetal from said metal deformation and said output thickness.
 12. Amethod of rolling metal according to claim 10 further includingadjusting the normalized force by an amount dependent upon the width andhardness of the metal being rolled before calculating said force ratio.13. A computer controlled method of rolling metal by passing said metalbetween a pair of confronting rollers whereby the incoming thickness,and therefore the amount of reduction, of said metal required to achievea desired magnitude of power for a given output thickness can bepredicted, said method comprising determining the temperature of themetal being rolled, accessing stored data depicting the variation ofpower for a predetermined percentage of draft as a function of outputthickness to determine normalized power required to obtain the desiredoutput thickness, calculating the ratio of the actual power to beapplied at said stand to the normalized power, accessing stored datadepicting the relationship between the ratio of actual power to thenormalized power as a function of a metal deformation factor selectedfrom the group consisting essentially of elongation and per unit draftto determine the quantity of metal deformation produced by thecalculated power ratio and determining incoming thickness of said metalfrom said determined metal deformation and said output thickness.
 14. Amethod of rolling metal according to claim 13 further includingadjusting the normalized power by an amount proportional to the widthand resistance to deformation of the metal being rolled and the speed ofthe stand prior to calculating said power ratio.
 15. An automatedrolling mill comprising at least one rolling stand having a pair ofconfronting rollers, means for adjusting the openings between saidrollers, and a computer control system having means defining a parameterselected from the group consisting of power and force by a first familyof curves defining the ratio of the parameter magnitude for a chosen perunit draft as a function of elongation, said family of ratio curvesbeing characterized by a common intersection at the chosen per unitdraft, means defining said parameter for a chosen per unit draft as afunction of the output thickness of metal passed through said stand,means for accessing said stored curves to determine both the value ofthe parameter for the chosen per unit draft required to produce adesired output thickness in metal passed through said rollers and thevalue of said ratio for a given elongation, means for calculating thearithmetic product for said values as determined from said curves, andmeans for predicting the selected parameter at said mill at thearithmetic product of said values.